A well-known example of global optimization that provides solutions within fixed error limits is optimization of functions with a known Lipschitz constant. In many real-life problems this constant is unknown.
To address that a method called Pareto-Lipschitzian Optimization (PLO) was described that provides solutions within fixed error limits for functions with unknown Lipschitz constants. In this approach, a set of all unknown Lipschitz constants is regarded as multiple criteria using the concept of Pareto Optimality (PO).
In this paper, a new version of the Pareto-Lipschitzian Optimization method (PLOR) is proposed where a set of unknown Lipschitzian constants is reduced just to the minimal and maximal ones. In the both methods, partition patterns are similar to those of DIRECT. The difference is in the rules of sequential partitions defining non-dominated sets. In PLO, it includes all Pareto-Optimal sets defined by all Lipschitz constants. In PLOR, it considers just two elements corresponding to the maximal and minimal Lipschitz constant. in DIRECT, it selects a part of the Pareto-Optimal set which is determined by some heuristic parameter .
It is important for an organization to know what capability/maturity of the process a chosen methodology could ensure. This paper is focused on DSDM Atern process maturity by CMMI.
The goal is to assess DSDM Atern by CMMI-DEV version 1.3 and propose the improvements to reach CMMI maturity level 3. A capability profile ensured by DSDM Atern has been obtained. The appraisal results showed that DSDM Atern ensures CMMI maturity level 2. Constraints and problematic areas of DSDM Atern methodology were discovered. In order to reach CMMI level 3 some recommendations for DSDM Atern additions were developed.
Computational modeling of a biosensor with allosteric enzyme layer was investigated in this study. The operation of the biosensor is modeled using non-stationary reaction-diffusion equations. The model involves three regions: the allosteric enzyme layer where the allosteric enzyme reactions as well as then mass transport by diffusion take place, the diffusion region where the mass transport by diffusion and non-enzymatic reactions take place and the convective region in which the analyte concentration is maintained constant. The biosensor response on dependency substrate concentration, cooperativity coefficient and the diffusion layer thickness on the same parameters have been studied.
In this research, parallel computing capabilities of MATLAB and the capabilities for the finite element method were analyzed. A program for solving a heat transfer problem by the finite element method was implemented. Three different parallel algorithms using CPU and GPU for solving steady state and transient heat transfer problems were proposed and implemented. A maximal speedup of around 2.3 times for steady state and 2 times for transient problem solving time was achieved by using a quad-core CPU.
This work contains Monte–Carlo Markov Chain algorithm for estimation of multi-dimensional rare events frequencies. Logits of rare event likelihood we are modeling with Poisson distribution, which parameters are distributed by multivariate normal law with unknown parameters – mean vector and covariance matrix. The estimations of unknown parameters are calculated by the maximum likelihood method. There are equations derived, those must be satisfied with model’s maximum likelihood parameters estimations. Positive definition of evaluated covariance matrixes are controlled by calculating ratio between matrix maximum and minimum eigenvalues.